Pulsating dynamics of thermal plumes and its implications for multiple eruption events in the Deccan Traps, India Urmi Duttaay and Nibir Mandal b a School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom b Department of Geological Sciences, Jadavapur University, Kolkata 700032, India Abstract In Earth’s mantle gravity instabilities initiated by density inversion lead to upwelling of hot materials as plumes. This study focuses upon the problem of their ascent dynamics to provide an explanation of the periodic multiple eruption events in large igneous provinces and hotspots. We demonstrate from physical experiments that plumes can ascend in a continuous process to form a single large head trailing into a long slender tail, typically described in the literature only under specific physical conditions. Alternatively, they ascend in a pulsating fashion, and produce multiple in-axis heads of varying dimensions. Based on the Volume of Fluid (VOF) method, we performed computational fluid dynamics (CFD) simulations to con- strain the thermo-mechanical conditions that decide the continuous versus pulsating dynamics. Our CFD simulations suggest the density (ρ∗) and the viscosity (R) ratios of the ambient to the plume materials and the influx rates (Re) are the prime factors in controlling the ascent dynamics. Conditions with large R (>50) develop pulsating plumes, which are sustained preferentially under low ρ∗ and Re conditions. Again, the increasing temperature difference between the plume and the ambient medium is found to promote pulsating behaviour. From these CFD simulations we show the thermal structures of a plume, and predict the peak thermal events near the surface that commence periodically as pulses with a time interval of 1.4-3 Ma. The pulsating plume model explains the multiple eruption events in the Deccan Traps in India, where the time scale of their intervals estimated from the available 40Ar/39Ar geochronologi- cal data shows an excellent match with our simulation results. arXiv:1703.00085v1 [physics.flu-dyn] 28 Feb 2017 Keywords: Analogue modelling, fluid, buoyancy, volume of fluid method, phase and ther- mal structures, CFD simulations, pulsating eruption events y [email protected] 1 Contents 1 Introduction2 2 Plumes in analogue models4 3 CFD simulations: the theoretical basis7 3.1 The VOF method . .7 3.2 Temperature dependent density and viscosity . .8 3.3 Model design . .9 3.4 Non-dimensionalization of the physical variables . 10 4 Simulation results 11 4.1 Ascent behaviour . 11 4.2 Threshold conditions for pulsating plumes . 14 5 Discussion 16 5.1 Geological relevance of the continuous and pulsating plume models . 16 5.2 Explanation for the pulsating plume dynamics . 17 5.3 Time scale of plume pulses and Deccan Trap eruption events . 18 6 Conclusions 21 1 Introduction Thermal plumes play a major role in controlling crucial geodynamic processes in the Earth, such as mantle upwelling from core-mantle boundary; melt advection beneath mid-oceanic ridges and evolution of large igneous provinces (LIPs) and hotspots [1–4]. These are initiated by Rayleigh- Taylor instabilities in hot, buoyant layers resting beneath a relatively cold, denser fluid. However, in some geodynamic settings, e.g. subduction zones plumes are driven by compositional buoyancy 2 forces [5,6]. Irrespective of their driving mechanism, plumes typically show bulbous heads trailing into slender, cylindrical tails. Turcotte and Schubert [7] have used Stokes formula to enumerate their ascent velocity as a function of density contrast and other physical variables, e.g., mantle viscosity and the size of plume head. Their theoretical work, however, applies to a steady state condition of the plume ascent, accounting a balance between the rate of material influx and the ascent rate of spherical head under constant shape and size. In reality, the ascent process is much more complex than that predicted from such a simple hydrodynamic model. Physical as well as numerical model experiments suggest their strongly unsteady state behavior, displaying transient responses to various physical and geometrical conditions [8–10]. Predicting such unsteady plume dynamics has opened a new direction of plume research in recent time. Earlier theoretical and experimental studies have recognized a range of physical factors, such as viscosity and density ratios between plume and ambient mantle [8, 11–16], and the role of ther- mal/chemical boundary layers (TBL and CBL) at the base [9, 10, 17], P and S velocity attenuation anomalies for modelling synthetic seismic plumes [18] and density stratification in mantle [19] that control the mode of plume ascent. For example, viscosity ratio (R) determines the magnitude of viscous drag exerted by the ambient medium to the rising plumes and thereby largely dictates their ascent modes, leading to either balloon- or mushroom-like single heads trailing into narrow tails [11, 15, 16]. Some workers demonstrated from experiments a completely different ascent dy- namics, where plumes form a train of heads of varying sizes, each of them migrate upward in the form of solitary waves [20,21]. A range of theoretical models have been proposed to explain such pulsating ascent behavior, e.g. shear flow along tilted tails [22] and temporal fluctuations in a con- duit flow, leading to solitary wave propagation [20,21,23]. Olson and Christensen [21] showed that long-wavelength solitary waves initiated by density-driven instability can travel through a vertical fluid conduit, confined by another fluid medium of higher viscosity. On the other hand, numerical models suggest that these solitary waves are actually conduit waves, which are formed when small diapiric bodies are continuously generated from TBL at the base of the existing plume and rise along the plume stem [23]. Despite significant progress in plume research, as discussed above there is a lack of systematic study of the hydrodynamic conditions in controlling the mode of plume growth- varying from a single, large head with a slender tail (continuous dynamics) to multiple heads in a train, ascending as solitons (pulsating dynamics). Our present study aims to address this issue, as it has significant implications in interpreting various geological phenomena, such as time-dependent variability of eruption activities and hotspot tracks, e.g. Emperor-Hawaiian island chain, Iceland, Yellowstone and episodic patterns of volcanic activities in recent and ancient LIPs, e.g. Columbia river plane, Deccan, Madagascar. These evidences strongly suggest the ascent of mantle plumes in pulses. 3 Schubert et al. [23] proposed a theoretical model to show the time scale of such pulses as a func- tion of mantle viscosity. Their model predicts a time scale of 9 Ma for viscosity ∼ 1022 Pa S, which decreases to 1 Ma when the viscosity is ∼ 1021 Pa S. The prime focus of our present work aims to recognize thermo-mechanical conditions that favour pulsating ascent of thermal plumes over con- tinuous, and also to characterize the frequency and timescale of such pulses. We demonstrate in analogue physical experiments these two ascent dynamics, and show their characteristic plume ge- ometry. The pulsating dynamics produces a train of in-axis multiple heads of varying dimensions. Using the VOF (volume of fluid) method we performed computational fluid dynamics (CFD) sim- ulations to evaluate the threshold physical conditions for the transition of continuous to pulsating plume dynamics. Using the simulation results we show maximum thermal peak events to occur periodically near the surface, and provide a time scale of such periodicity in thermal events. The cretaceous Deccan Trap has been reported to have evolved in multiple eruption events [24, 25]. The available 40Ar/39Ar geochronological data suggest a time scale of their intervals as 1.1-2.1 Ma. Using the pulsating plume dynamics we model the multiple eruption events in the Deccan Traps, and explain the time scale of their eruption events. 2 Plumes in analogue models Using an analogue modelling approach we investigated the ascent behaviour of thermal plumes in laboratory experiments. The experiments were performed in the following way. We chose transparent glycerin (viscosity 0.8 Pa S, density 1260 kg/m3) to simulate the long time scale fluid behaviour of Earth’s mantle. This kind of low-viscosity fluids has been widely used for plume and convection experiments in geosciences [26]. The glycerin shows strongly temperature dependent viscosity. We took a volume of glycerin in a glass-walled tank (12 cm×6 cm×8 cm) which con- tained a small passage (diameter ∼ 4 mm) for injecting fluid through the base. In the beginning the tank was subjected to heating in order to keep the base at an elevated temperature of 45◦C. The top surface of the glycerin column was exposed to the ambient temperature (∼ 29◦C). Using thermo- couples we monitored the temperature of glycerin varying with depth. When the experimental setup attained nearly a steady state thermal state, we injected into the tank the same glycerin, but of varying temperatures through the passage at the tank base. The injected fluid was coloured to make the plume structures visible through the transparent ambient medium. We also used engine oil (viscosity 0.155 Pa S; density 872.5 kg/m3) as an injecting fluid into the glycerin medium for a different set of experiment. The oil viscosity decreased rapidly with increasing temperature. A summary of the experimental data is given in Table1. We captured the images of evolving plume structures during an experimental run, keeping the camera at fixed focal length. 4 Figure 1: Development of thermal plume in analogue models - continuous (top) and pulsating (bottom) ascent dynamics. A-E denote progressive stages in each case. A set of experiments was performed with an injecting fluid of higher temperature (∼ 60◦C) than the ambient. The experiments produced plumes, which continuously ascended through the ambient medium to form a single structure with big head and slender tail (Fig.1 top row).